Geodesic
On a Class of Graphs with Large Total Domination Number
Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 1

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Let $\gamma(G)$ and $\gamma_t(G)$ denote the domination number and the total domination number, respectively, of a graph $G$ with no isolated vertices. It is well-known that $\gamma_t(G) \leq 2\gamma(G)$. We provide a characterization of a large family of graphs (including chordal graphs) satisfying $\gamma_t(G)= 2\gamma(G)$, strictly generalizing the results of Henning (2001) and Hou et al. (2010), and partially answering an open question of Henning (2009). 
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     author = {Bahad{\i}r, Selim and G\"oz\"upek, Didem},
     title = {On a {Class} of {Graphs} with {Large} {Total} {Domination} {Number}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
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     year = {2018},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-20-1-23/}
}
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Bahadır, Selim; Gözüpek, Didem. On a Class of Graphs with Large Total Domination Number. Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 1. doi: 10.23638/DMTCS-20-1-23

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